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In this essay, I argue that modern science is not the dichotomous pairing of theory and experiment that it is typically presented as, and I offer an alternative paradigm defined by its functions as a human endeavor. I also demonstrate how certain sci- entific debates, such as the debate over the nature of the quantum state, can be partially resolved by this new paradigm.

Author Bio

Ian Durham is an Associate Professor of Physics at Saint Anselm College where he has served as Chair of both the Physics and Mathematics Departments and as Director of the Computational Physical Science Program. He is a member of FQXi.

You leave me unconvinced that you have successfully defended reductionism. I like your statements about what it is not, and how it is a term often misapplied to methodologies that are not, at their heart, reductionist. But you have perhaps created another form that is not - strictly speaking - reductionism either, and is rather an argument that to employ reductionist methods we...

You leave me unconvinced that you have successfully defended reductionism. I like your statements about what it is not, and how it is a term often misapplied to methodologies that are not, at their heart, reductionist. But you have perhaps created another form that is not - strictly speaking - reductionism either, and is rather an argument that to employ reductionist methods we need to allow diversity of interpretation - so it is a kind of expansive reductionism. I think perhaps the fault lies in the objectivism implied by defining Science as measurement, description, and predictive explanation - which ultimately disallows anything but a reductionist view.

The quote from Jaynes "the world is too complicated for us to analyze it all at once. We can make progress only if we dissect it into little pieces and study them separately" is something that is absolutely true only for those whose brain has a non-functioning right hemisphere. Fortunately; the rest of humanity does have a cognitive apparatus that continuously presents us with the view that reality exists as a congruent, whole, and unified reality. Simply put; while the left brain likes to take things apart and look at the pieces, the right brain likes to assemble the pieces instead. Of course this is oversimplified, but details can be found in this paper.

The point is that reductionism is not time-reversible, but rather inference is the inverse operation of reductionist methodologies. So you may have shown the exact opposite of what you claim to prove. To further elaborate on the point of how your definition of Science requires a reductionist view, I recall a discussion in a paper by Connes (which I will find and post a link to) about smooth, topological, and measurable spaces - that I think has some relation to questions about objectivist Science as well.

A smooth relation may result in things being blended, so that objects and categories are less strictly defined, and are not clearly distinguished one from the other. Topology allows the property of sharp distinctions to arise, so that things, categories of things, and spaces, can be more clearly distinguished from each other. If we allow topological objects the property of separability, only then do we see the possibility for measurement, as such, to arise. So attempting to apply a reductionist standard, which assumes the properties of independent object to be extant, and then to require that there be a smooth relation between alternate descriptions, would appear to be another form of the same misapplication of reductionist terms (a la Lehrer), or a subtle duplicity.

So is there a single answer to which things can be reduced. No! And it would appear that you leave reductionism in doubt.

I think you have partially missed my point. My suggestion that quantum mechanics might need multiple interpretations was precisely that: a suggestion. It was a far cry from the primary point of my essay which was that the old theory/experiment duality is not an accurate paradigm for describing science.

As for your continuing doubts about reductionism, I would be shocked if one eight-page essay by one person could definitively eliminate all doubts. My point about reductionism is that the anti-reductionist argument appears to be based entirely on an a priori assumption that the world is simply too complex to be explained by reductionist methods. In other words, anti-reductionism's argument against reductionism begins by assuming the latter is wrong to begin with. That's an argumentum ad ignorantiam: it assumes something is false simply because it has not been or cannot be proven to be true.

By better understanding the role of mathematics in science (and in the nature of the universe itself), I think it is too early to sound the death knell on reductionism. In fact I find it down-right dangerous since it opens the door to things like intelligent design which have no place in science.

Incidentally, reductionism does not mean that we are not interested in fully comprehending the whole of something (that's another inaccurate accusation lobbed at reductionists). Yes, sometimes the whole has properties whose meaning may be more than the sum of the meaning of its parts, but meaning is not the same thing as function. Meaning is not the realm of science, it is the realm of philosophy (which is not a bad thing, by the way).

Ian

Author Ian Durham replied on Sep. 4, 2012 @ 20:04 GMT

Oops! The first sentence in the third paragraph should have said:

"By better understanding the role of mathematics in science (and in the nature of the universe itself), I think we may find that it is too early to sound the death knell on reductionism."

Author Ian Durham replied on Sep. 4, 2012 @ 20:17 GMT

Let me add one more thing that was perhaps not made quite clear. There seems to be this assumption that reductionism automatically precludes more holistic approaches. But that's absurd. I can fully understand a car via reductionist methods, but understanding its purpose is still holistic. The holism comes from putting the pieces together. Perhaps a better example is a finger: a can dissect a finger and learn all sorts of wonderful things, but I still won't understand what causes it to move until I understand how the muscles and nerves are connected with the rest of the body. And yet I'm still using a reductionist method here.

I appreciate the well-considered reply. I probably grasped more of your argument than it would appear, but I was feeling feisty (or wanted to play devil's advocate), and I have long believed that reductionism should itself be subject to the reductionist method, which to me means it should be taken apart.

The thing is; if we were successful at completely dissecting reductionism, I suspect it would be like a watch once taken apart, with the pieces spread out on the table. Of course; in that condition it would no longer function. So we need to be able to assemble the watch as well, before we can claim to actually understand how it works.

But I will grant that you have apparently showed we can assemble reductionism a bit differently, so it actually works as intended. In that case, reductionism is not dead - but was merely in need of repair.

Agreed. Personally, I *do* think there is a limit to reductionism, but then I also believe there is a limit to what we can possibly know about the universe since we are a part of that universe and cannot view it entirely objectively.

Thomas Howard Ray replied on Sep. 12, 2012 @ 12:25 GMT

Hi Ian,

You preempted a lot of what I would have said about your splendid essay, here and in discussions on George Ellis's site. "There seems to be this assumption that reductionism automatically precludes more holistic approaches. But that's absurd. I can fully understand a car via reductionist methods, but understanding its purpose is still holistic. The holism comes from putting the pieces together."

Indeed. Personally, I think the modern reductionist paradigm amounts to what I call reduction to complexity. I'm not willing to give up my own reductionist tendencies (I think you might agree that few research mathematicians are). I'm reminded by your example above, that Einstein allowed that a symphony might be described in terms of variations in sound wave pressure, yet that would not convey the meaning of a symphony. Meaning and reductionism do not have to be at odds.

Best wishes in the contest! (And I hope you get a chance to visit my own essay, "The Perfect First Quesiton.")

Anyway, I appreciated your original comments. It's always good to poke holes in arguments. It's the only way we can know if we have made a mistake or not (and, it could be argued, is a reductionist method!). I don't mind feistiness as long as it is polite and free from vitriol (which your comments were).

I will add it to my "to-read" list. (At some point, in a more private setting, I should ask you where in Upstate NY you are from...).

Vladimir F. Tamari wrote on Sep. 5, 2012 @ 01:18 GMT

Dear Ian

I enjoyed reading your lucid and well-reasoned essay and Jonathan's retorts. As an Arab (my Russian name notwithstanding!) I laud your placing Ibn Al-Haytham where he belongs - at the beginning of any historical discussion of the scientific method. Sadly most such discussions start with Galileo ignoring Al-Haytham's pivotal contribution. Having said that, and having read his Kitab...

I enjoyed reading your lucid and well-reasoned essay and Jonathan's retorts. As an Arab (my Russian name notwithstanding!) I laud your placing Ibn Al-Haytham where he belongs - at the beginning of any historical discussion of the scientific method. Sadly most such discussions start with Galileo ignoring Al-Haytham's pivotal contribution. Having said that, and having read his Kitab Al-Manather (Book of Optics) in Arabic I wonder if it is correct to compartmentalize his method into just theory + experiment. There is also his meticulous systematic analysis and clear description, precursors of modern scientific writing. Considerable interplay between his theories and experiments is obvious in his writing. His observations of natural phenomena, not just in experiments, and his mulling these things over cannot be neatly put into these two pigeonholes. In any case his speculations did generate the predictive explanation that you spoke of: he used his experiments with the camera obscura and theoretical analysis of light rays to explain vision.

You explained the difference between statistics and probability very well. I have definite bias against the use of probability as a causal explanation of Quantum phenomena (see my papers below).

Thank you for explaining the nuances of the term reductionism as used these days. I wonder how you would describe such work as Stephan Wolfram's A New Kind of Science - where one starts from a model and builds upwards using mathematical and computational tools. My Beautiful Universe Theory on which I based my fqxi essay Fix Physics! might go under that category. Constructivism seems a nice word to desribe such work, but again there is that interplay between the model and what one knows of physics - a lot of hidden intuitive ideas working themselves out into theory...and experiment, and predictive explanations.

Thanks for the nice comments! I must admit that I am not as familiar with Al-Haytham's work as I probably should be. That being said, I think that it's really the people who came after him and re-interpreted his work that distilled it into theory and experiment. As with everything, when we do something our intentions and motives are always more complex than they are later remembered. In other words, history has a bad habit of over-simplifying. So I think you are correct in saying that his work is considerably more nuanced than history has made it out to be.

In a serious sense anti-reductionism is a straw man. Practically, realistically, there's no other way to do experimental science except analytically. Scientists (and there'll always be those people because folks need to do something with their lives) will continue to employ reductionist methodologies because what's the alternative? Or at least they'll continue until they discover they no longer can, at which time the paradigm will shift big time anyway.

It's sort of like inveighing against postmodernism. Corrupting the minds of an entire generation, of the whole intellectual class! Not so much. Besides, a lot of the funding's dried up.

(1) "We are inherently assuming, here, that mathematics can fully describe physical systems. This may or may not be true, but for now we assume that it is.

(2) But mathematics is built on logic and is thus internally completely self-consistent. In other words, mathematics is and always has been assumed to be purely reductionist."

Euclidean mathematics was abandoned by Dedekind and others and has been considered internally completely self-consistent since then. If "measurement, description, and predictive explanation ... are the essence of reductionism" then [2] might be questionable.

May I infer that Euclidean mathematics still included a sound and necessary restriction to pure reductionism?

I consider IR+ and IR equally based on logic and therefore completely self-consistent in principle.

I even suspect that some obvious to me imperfections of mathematics (for examples cf. topic 833) resulted from a brutal pseudo-reductionist pseudo-holism (infinitum creatum sive transfinitum) in mathematics.

Nonetheless, I see Durham's essay not just excellently written but even more importantly a relevant revelation of a wrong fundamental assumption.

I would certainly defend the intellectual necessity of reductionism, even to the point of describing it as a reflection of natural processes, as evidenced by some of the colloquial terms applied to it, such as distill, condense, focus, etc. As one might distill out the salient points of interest, or condense an argument to its irreducible points.

I would certainly defend the intellectual necessity of reductionism, even to the point of describing it as a reflection of natural processes, as evidenced by some of the colloquial terms applied to it, such as distill, condense, focus, etc. As one might distill out the salient points of interest, or condense an argument to its irreducible points.

I would argue that statistics and other forms of generalization are a form of reductionism. One is simply distilling out the relationships within a larger set, rather than focusing on all the details involved. Your distinction between statistics and probability proves the point, since statistics is the set of the known, as distinct from possible consequences. A fully wholistic view would not be able to make that distinction and that is the problem with true wholism. It entails all connections and relationships, without the conceptual necessity of defining/focused sets. Much as a camera shutter left open would collect far more information, but lack clarity.

The intellect evolved out of the biological necessity of navigation by mobile organisms. Its fundamental function is to make decisions, even when the situation isn't clear. It is digital in an analog reality.

This requires reductionism of information, whether to specific details, or to generalizations. The left, linear hemisphere is better at details, while the right, instinctive side is better at generalizations. It might appear wholistic, because it deals in masses of information, but the purpose is to reduce that mass down to such binary concepts as good/bad, left/right, up/down, yes/no, 5 to 3 odds, etc.

I would also comment that the distinction you make between statistics and probabilities goes to one of the main topics usually discussed at FQXi and physics conversation in general and that would be the issue of time. Statistics only applies to what is known, ie. the past. While probabilities apply to how they might be applied, ie. predicting the future. Now consider the difference between how we acquire statistics from probabilities, vs, how we apply statistics to better understand probabilities. We acquire statistics by observing events as they happen, ie, what was future probability becomes past statistic. Now we go the other direction when we apply statistics to probabilities, we use the past to predict the future.

In my essay, the problem I point out in physics is that we only think of time in terms of how the past is used to define the future, ie. going cause and effect. Yet the physical reality is of the future becoming past. In other words, we treat time as a narrative process from past events to future ones, but the physical process is one of dynamic change that collapses probabilities into actualities. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. So rather than going from a determined(statistical) past into a probabilistic future and ending up with multiworlds, it is the collapse of probability which yields actuality. A large part of the confusion is that cause and effect isn't sequence, but energy exchange. Yesterday doesn't cause today, any more than one rung on a ladder causes the next. It is the exchange of energy, such as sunlight shining on a rotating planet, that causes the sequence of events called 'days.'

The problem is that physics goes from measurement to description and then to predictive application, without fully considering what is being measured. The same issue created the problem of epicycles and a geocentric cosmology. By measuring the action of the various heavenly bodies, ancient cosmologists developed an accurate description of their actions, such that it had predictive powers as to where those bodies might be in the future. This then created the impression that the model and its physical explanation, giant cosmic gearwheels, was true. Any anomalies were simply considered to be due to undiscovered gears and the search would be to figure out where they would be. What was overlooked was simply that the earth is also a body in motion and when Galileo placed it on orbit around the sun, everything else made more sense. Now we treat time as a series of events, because that is the foundation of our intellect, from narration to cause and effect, just as the earth is our physical foundation. But it is the process creating those events which is foundational, yet physics is more focused on the details of ever more precise measurements of events, not stepping back to see the broad picture of what causes them. So motion is ascribed to the present along the timeline, rather than the events through the present.

The present isn't some dimensionless point on a timeline, because duration doesn't exist external to the present, but is the state of the present between measured events.

One field of study that further clarifies this distinction between the determined past and the probabilistic future is Complexity theory, with order as the known and chaos as the random. Which is another example of the relationship between statistics and probability.

Thanks for those comments. I fundamentally agree with your first few paragraphs. I'll have to think about the rest. Certainly some of the ideas in my essay were born from last year's FQXi conference on time and many of these ideas (including those relating to complexity) were discussed at length.

And I would agree that statistics can be a part of reductionism (in fact I argued that to some extent in my essay in that I include it in the mathematical piece). I'll have to think about the rest. ;)

Ian

John Merryman replied on Sep. 8, 2012 @ 16:46 GMT

Ian,

Thank you for the response. I have to say I frequently get negative reaction to this point about time, without much reasoned response. I think a significant part of that is it requires examining the serial foundation on which knowledge rests. As a cardiologist neighbor of mine once responded, when I made this point, "Stop it. You're hurting my head."

Thanks for your deeply original article. According to me,as you feel,reductionism has its own limitations when applied to science as a whole. For example,you can apply reductionism to physics to any limits i.e.,as long as you can reduce all the four fundamental physical forces to one unifying force. But the same thing doesn't work with biology and its related sciences.This is simply because you got to take in to account 'Evolutionary Traits' like the emergence of intelligence,consiousness and the like.So as a result of which you cannot explain the behaviours of more complx organisms like humans on the basis of simpler organisms like amoeba and the like.

Now coming to the various interpretations of Quantum-Mechanics, I too have my own interpretation of Quantum-Mechanics and it can give some different insights in to the quantum world not given by other versions of QM. For this,please,go through my essay (http://fqxi.org/community/forum/topic/1543--Sreenath B N.) and later I give you an equation following from my version of QM and which cannot be derived from other versions of QM.

I read your insightful essay with great interest. Contrary to what has been stated by another commentator, my position is that you cannot apply reductionism to any limit in physics. Limits to reductionism starts in physics itself. Then when it goes to the next higher levels, the relation between the parts and the whole becomes even more complex.

I read your insightful essay with great interest. Contrary to what has been stated by another commentator, my position is that you cannot apply reductionism to any limit in physics. Limits to reductionism starts in physics itself. Then when it goes to the next higher levels, the relation between the parts and the whole becomes even more complex.

Nevertheless, reductionism is a human epistemological tool which cannot be dispensed with however much we fight against it. Human knowledge develops through the combined process of analysis and synthesis. Dismissing reductionism is like throwing the baby with the bath water.

But in using this tool we have to understand that there is a discrepancy between mathematical parts naively conceived, and their empirical counterparts.

A photon breaks up into an electron and a positron is pair production. We find that the sum of the two parts is greater than the whole that broke up into two.

In discussion of thermodynamics, a popular example of irreversibility is a broken cup, which cannot be restored to the original state by putting the pieces together. Why they cannot be brought together is that in the break up process the pieces gain energy from the field. With this gain of energy their innate cohesive power to stick to one another is lost.

Nature’s way of cohesion is extraction of fractions of energy from the parts, and their mutual deficiency is overcome by sharing their intrinsic energies and forming a whole body. This is why we find in nature that the sum of the energy of the parts is always greater than that of the whole. In the reverse process, when a whole breaks up into parts, there is an influx of energy from the field causing a repulsion between the parts.

In relativity we have two gamma-factors. We come across the first in say the expression of kinetic energy = Mc2[ 1/(1- v2/c2)1/2 – 1)]. Here v is the velocity of the particle. This gamma-factor arises due to loss of fractions of energy when Mc2 and pc (in the energy-momentum equation) fuse together to form a system.

The second gamma-factor = 1/(1-u2/c2)1/2 we come across in the Lorentz transformation. Here u is the “velocity of the reference frame” (not the velocity of the particle). This is the result of breaking up of the energy into two parts (as I explain in my essay) and this is the factor by which parts gain energy.

So we have to use the tool of reductionism knowing that there is a process going on which is not representable by linear addition. It is trigonometric. This process is dealt with in my essay in –Geometrodynamics.

I request you to have a look at my essay: http://fqxi.org/community/forum/topic/1549

As I advocate modelling, testing and pattern matching, I agreed with your thesis, but it was also well described and argued. I also agree with the 3 part view; measurement (quantification), description, and predictive explanation, and;

"it aims for logical self-consistency with the crucial additional assumption that science, as a whole, is ultimately universal. This last point implies that all of science is intimately connected."

Using that approach my own essay seems to represents a proof of your views, showing how a 'reductionist algorithm' in terms of a combination of real quantum mechanisms can use a logical (TPL) structure to build a complex ontological construction able to derive the macro classical universe directly from the quanta. i.e. the SR postulates, (inc. CSL) and space-time from dynamic evolution of wave-particle interaction.

I proposed to Julian that any correct model must describe the universe at all scales, so holism is not sacrificed, and even a pre 'big bang' condition emerges from a better 'all scales' interpretation. I've failed to falsify it, so hope you can study, comment, and either do so or use it's predictive powers.

Last year you replied to me "I don't think anything will truly change until there is a major breakthrough in experiment." Look at Fig 2 of Rich Kingsley-Nixey's essay, showing the results of the massive Cluster probe 'experiment'; the real boundary condition I invoke for mutually exclusive states, simply requiring the better more logically consistent interpretation he also finds.

You did not appear to (one of the few it seems) read my essay last year ('2020 vision' 7 behind yours). I hope you might now for background as only the tip of the iceberg fits in 9 pages.

I think you deserve to better your last years finish. I look forward to your views on mine (beneath the layer of Theatre).

I agree with your sentiments wholeheartedly regarding holism. I will add your essay to my list and hope to get to it soon. I got through a couple and then got crazy busy with some stuff. But I hope to get back to reading them next week sometime.

Ian

Member Ken Wharton wrote on Sep. 20, 2012 @ 21:18 GMT

Hi Ian,

Nice essay! I particularly liked the point that "description" and "explanation" are both important aspects of science, and are distinct activities. (There's probably some mileage to be had in exploring how one generation's explanation is the next generation's description, which in turn needs a deeper explanation, but I agree with you that these are nonetheless generally distinct functions of science, and should be viewed in that light -- as you argue.)

My one quibble has to do with the sudden appearance and use of the word "predictive" (no surprise there, I'm sure!). You didn't spend much time justifying it, as prediction is evidently important, but I wonder how you would feel about moving the adjective "predictive" over to the "description" camp. In other words, instead of distinguishing "description" vs. "predictive explanation", what about distinguishing "predictive description" from "explanation".

After all, the word "description" implies that one is conveying some fact about reality to us humans, and to us, the most useful descriptions will be predictive. Meanwhile, ultimate explanations are (I hope) completely blind to whether humans even exist or not, so limiting scientific explanations to only predictively-useful ones seems overly restrictive. And of course I'd hate to think you're ruling out my preferred explanation of quantum phenomena by mere fiat -- or, at least, not without a good stiff argument! :-)

As I mentioned during our Scrabble game, I swear yours is next on my to-read list. ;)

Anyway, I actually disagree with you about where the word 'predictive' belongs. I don't see descriptions as being in any way predictive. A description is precisely that: a description. What allows us to make inferences from descriptions is the associated explanation. For example, suppose I have just landed on a deserted island and found an animal (maybe one I've never seen before). Suppose it has two tails. Can I properly infer that all such animals have two tails? How do I know what is an anomaly and what is not? I can't make any solid inferences without additional data (more examples of the animal). In fact, the mere act of making an assumption or inference immediately implies that you are inherently providing an explanation of sorts because there has to be something behind your assumption. So if I assume all such animals have two tails, my explanation is that all such animals look the same (or even more simply, that they all must have two tails!). Do you see what I mean? Description just describes. As soon as we make any kind of assumption, we are "predicting," whether or not we realize it.

Now, as for your preferred explanation of quantum phenomena, I don't necessarily think I'm ruling it out. How do you know your explanation (I assume you're referring to your final boundary condition one, right?) won't turn out to be predictive as well as descriptive?

Ian

Author Ian Durham replied on Sep. 21, 2012 @ 02:26 GMT

Oh, and thanks for the compliment (that was rude of me to forget to say that - my mother taught me better - but it's late and I'm falling asleep...). ;) Seriously, thanks, I appreciate that you liked it.

Richard William Kingsley-Nixey wrote on Sep. 22, 2012 @ 12:42 GMT

Ian

High quality essay. Perhaps a hard battle to win, but Peters essay, 'Much ado about nothing' (but really everything) is consistent with mine and both seem to show that reductionaism does produce the goods, producing classical observation, or the SR posultates, from applying logic to quantum mechanisms. In a way both also use the 'top down' or at least 'holistic' approach to reductionism. Do please give your views.

Very well written! In addition to the interesting nature of the topic (particularly to someone like me), I appreciate the general viewpoint and broad historical and philosophical context. I have a few questions and remarks:

1. On page 2, you note the close relationship between causality and the “reduction” of a system to its “constituent parts,” and on page 4,...

Very well written! In addition to the interesting nature of the topic (particularly to someone like me), I appreciate the general viewpoint and broad historical and philosophical context. I have a few questions and remarks:

1. On page 2, you note the close relationship between causality and the “reduction” of a system to its “constituent parts,” and on page 4, you mention several possible views on the independence of “emergent behavior” from “underlying processes.” You then proceed to offer two objections to what you call the “anti-constructionist view” asserting a degree of independence in this sense. In this context, and avoiding for the moment quantum-theoretic complications, I would offer a third objection, which I also mentioned to George Ellis. Causality is also closely linked to “the” arrow of time, and causality is often described in terms of a binary relation on the set of events (this relation is defined in terms of the light cones in special relativity, for instance). Now if emergent systems exert causal influence independent of their constituent events, then one must model causality not as a binary relation on the set of events (of a classical universe), but as a binary relation on the much larger set of subsets; i.e., the power set. Causality would then represent an “arrow” (i.e., a single dimension) only from the perspective of the power set of the universe, while at the level of the universe itself, it would appear vastly more complicated and nothing like the arrow of time we seem to observe.

2. I am not sure what you mean by the statement that mathematics is purely reductionist? Your brief explanation is that mathematics is “built on logic and is thus internally completely self-consistent.” Ignoring possible Godel-type objections to this, I would point to the structure I described above (a binary relation on a power set) as something I would call a non-reductionist mathematical system: by definition you cannot tell what is happening by looking at pieces of a given subset, since the subset is assigned its own “point” in the power set, and information can be assigned to this point which has nothing to do with the information assigned to the points representing the individual pieces. An analogous example in a totally different field of mathematics is the concept of a positive-dimensional point in an algebraic scheme in algebraic geometry; one of the most important conceptual aspects of Grothendieck’s program was the realization that working only with the zero-dimensional points leaves out important information.

3. It seems that all this becomes much more complicated when one attempts to combine quantum theory and general relativity. In his 1948 paper, Richard Feynman discussed summing over particle trajectories in Euclidean spacetime and thereby recovered “standard” quantum theory, with its Hilbert spaces, operator algebras, Schrodinger equation, etc. Feynman was able to take all the trajectories to be in the same space because he was working with a background-dependent model; the ambient Euclidean space is unaffected by the particle moving in it. Now, if GR has taught us anything, it is that “spacetime” and “matter-energy” interact, so that different particle trajectories mean different spacetimes. Hence, in a background-independent treatment, Feynman’s sum over histories becomes a sum over “universes,” with a different classical spacetime corresponding to each particle trajectory. His original version is a limiting case in which the effect of the particle on the spacetime is negligible. Now, from such a perspective, the phases associated to the paths, and hence the amplitudes, a priori depend on the entire universes involved. Thus, it seems that holism can arise as a quantum phenomenon even with a completely reductionist classical theory.

4. These two features, complete reductionism at the classical level, with holism in the above sense arising at the quantum level, represent the only way I can think of to move toward a suitably relativistic and quantum theoretic picture, as I describe here in my essay: On the Foundational Assumptions of Modern Physics. Reductionism seems necessary at the classical level to make sense of time and causality. Holism seems necessary at the quantum level because the sum over histories method is the only version of quantum theory I know of that seems to generalize in a suitable manner to the nonmanifold models of spacetime that seem likely to be relevant for quantum gravity.

Evidently you have thought about these issues deeply and in a wide range of contexts, and I would be grateful for any further remarks you might have. Take care,

I have a very tough question for you. Does a reductionist mindset adversely affect funding for scientific research, or is it mainly the false application of reductionist methods that leads governments and foundations to limit research funds to a few promising possibilities - on the basis that there is only one correct answer? People with a background in Economics seize on this...

I have a very tough question for you. Does a reductionist mindset adversely affect funding for scientific research, or is it mainly the false application of reductionist methods that leads governments and foundations to limit research funds to a few promising possibilities - on the basis that there is only one correct answer? People with a background in Economics seize on this observation, citing the purely reductionistic nature of ordinary Maths.

But as Ben pointed out above; there are areas of Math where this does not apply. One could start with the assertion by Connes that "Noncommutative measure spaces evolve with time," but as I point out in my essay, there are wild places beyond that. Ben's statement from Grothendieck - that points leave out too much information - was probably the motivation for Penrose to create Twistors, where Rays are fundamental instead of points. But the Octonions drive a kind of ordered evolution that I've come to fancy, as my essay also mentions, and some folks say they are the most general algebraic number type. Somehow the idea of one right answer does not apply there, as one can typically use any one of 16 multiplication tables, so long as you are consistent. But I digress...

Where the mindset of reductionists is to take things apart to see their smallest components; it is no wonder that String Theory has appeal for those whose job is to decide who - or what - gets funding. It is the ultimate in reductionistic mania, purporting to describe the smallest possible constituents of matter. And what is more; they are things! So it demands no higher level of abstraction of the grant reviewer, than a different kind of object that is very small and vibrates in 10 dimensions (and we don't know why it's 10, but we know it has to be that way).

So I posit that the reason String Theory has taken a lion's share of the funding pie for theoretical Physics, is that the folks who divide the pie are - by and large - materialistic reductionists, who are heavily invested in what de Bono refers to as "vertical thinking" rather than "lateral thinking." In my essay; I argue that scientists must be playful - and willing to explore many untried possibilities - in order to win the gold of scientific progress and research breakthroughs. But reductionists controlling the funding could defeat any such initiative, and stall the engine of innovation.

This is why is was so hard for me to read that the Science ministry in Spain was turned over to the Minister of the Economy, whose first act was to close several 'under-performing' laboratories - which were then liable for repaying their funding, though in some cases no research was performed or results obtained, because they were halted before that point. So was this a mis-application of reductionism, by someone who doesn't know how progress is made in Science? And how bad of a problem do you think this is for Science funding in general?

I wanted to mention that I enjoyed your essay greatly, Ian, and that I also fully understand what a useful and essential tool reductionism is. But it's part of a duality; formant synthesis and additive synthesis can yield the same result, and our brains are wired to give us both a fragmented and a holistic view simultaneously.

So people who have conveniently tuned the creative portion of their brain out, in order to function in a world of Finance which demands absolute reductionism, have a hard time understanding why research is better handled in a way that is more open-ended for the researcher. We should consider, however, what actually works.

I cite Doug Osheroff, in my essay, as an example of the playful approach that encourages one to look where nobody has looked before (and he won the Nobel). But people of a cautious mindset borne of years of exclusive dedication to reductionism find the whole idea of a playful approach distasteful, as it equates with 'just fooling around' instead of 'serious Science.'

I find your writings to be fruitfully insightful. By this I mean that you communicate your insights in a not so individual-matter-of-fact manner that I feel is all too common. But, rather state them so that their potential extends beyond your own statements and are adaptable to the thoughts of others.

My opinion about emergent properties is an individual-matter-of-fact opinion. I see it as the theorists' rationalization of their failure to achieve theory that predicts such properties. The temptation to believe, and act as if, we are near the end while still only scratching at the surface is an assumption that I feel needs to constantly be refuted with revision, including deletion, of theory while also adding the many missing parts at all levels. I am expressing only my own opinion.

I apply your statements to my own ideas while still reading yours. My thoughts undergo reorganization and alteration perhaps becoming potentially more accurate and more thoughtful in presentation. I revise theory at the introductory level. I already want to re-write my essay.

Aside from what I think about theory, for professionals I feel that your method of presentation contributes to stimulating scientific progress. Your essay deserves higher rating than its present position. Good luck in the contest.

I want to let you know that I read your essay some time ago and have just taken another look at it. It is very good. Though I must agree with Tom's comment that it does not have to be acceptance or rejection of reductionism. There are situations where consideration of complexity is more useful than reductionism, (such as when thinking about an organism or an organisation,...

I want to let you know that I read your essay some time ago and have just taken another look at it. It is very good. Though I must agree with Tom's comment that it does not have to be acceptance or rejection of reductionism. There are situations where consideration of complexity is more useful than reductionism, (such as when thinking about an organism or an organisation, or ecosystem, selection of whole macroscopic forms or populations or the role of information within structures). You point out larger arrangements can always be reduced to their constituents. I mention in my essay that that does not necessarily provide better explanation of what is occurring.

I agree with many of the things that you have said such as,

Quote:"The aim of theory, on the other hand, has always been to explain the world around us and not merely to describe it. What sets modern theoretical science apart from Aristotelianism and other historical approaches is that it aims for logical self-consistency with the crucial additional assumption that science, as a whole, is ultimately universal. This last point implies that all of science is intimately connected. Thus we fully expect that biological systems, for example, will still obey physical and chemical laws. Crucially, modern theoretical science also aims to predict the future behavior of systems. Thus a 'good' scientific theory is both explanatory as well as predictive."

That ideal blend is what I have been striving to accomplish.

You wrote, Quote "Finally, if we then return to the problems of complexity and emergence, if science is to be considered universal, connective, and self-consistent, perhaps the problem is not that reductionism is a broken paradigm, but rather that we are mis-ascribing some of our activities to the wrong scientific function, e.g. perhaps some of our so-called theories are actually more descriptive than predictively explanatory." I agree that is important to consider.

I especially agree with your conclusion, the importance of that introspection necessary to keep science vital and relevant. Thank you for sharing your points of view.I enjoyed reading and thinking about them. Good luck in the contest.

I very much enjoyed your essay. You did an excellent job describing 'probability and statistics' -- two words that often go together and may be naively interpreted to mean pretty much the 'same thing'. I appreciate your emphasizing the difference in meaning of these terms.

I also liked your summary of interpretations of quantum mechanics as 1.) statistical, derived from measurements, and 2.) epistemological, a state of knowledge that can be updated, ie, probabilistic, or 3.) ontolological, ie, descriptive of the real state.

I have a slight variation on these, linking the ontology of a real wave to the probability associated with FGourier analysis in Hilbert space, ie, the wave function. I hope you will read my essay, The Nature of the Wave Function, and comment on it.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material (definition from the ABSOLUTE theory of me) - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is

and

was the quantity of people which gave you ratings. Then you have

of points. After it anyone give you

of points so you have

of points and

is the common quantity of the people which gave you ratings. At the same time you will have

of points. From here, if you want to be R2 > R1 there must be:

or

or

In other words if you want to increase rating of anyone you must give him more points

then the participant`s rating

was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

This implies that the current statistical methods and computations, needs new algorithms to experiment theoretical updates for validations. Thus the probabilistic nature of quantum computing may be reduced on considering the dynamics of string-matters expressional on this paradigm in that dimensionality emerges with string-dynamics and reductionism is much applicable to express complex things.